Ordering Methods of C-Control Charts With Interval Type-2 Intuitionistic Fuzzy Sets

Demiralp, Sibel; Haçat, Gülnur

doi:10.33773/jum.679853

Cited by 2 publications

(3 citation statements)

References 10 publications

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“…if A ⊂ X then it is defined by the functions µ A (x) and ν A (x). In the literature [21]- [41] the such type objects as A are called intuitionistic fuzzy numbers. Taking into account that in the previous section we called so (very reasonably) the objects of a different kind, here we will call objects of type A defined by µ A (x) and ν A (x), intuitionistic fuzzy values (IF V ).…”

Section: New Representations Of Peace-wise Membership and Non-membership Functions Their Interval Extensions Based On The Revealed Sourcementioning

confidence: 99%

“…As it was stated in the previous section, one of the problem of the known IF V definitions [21]- [41] are the controversial asymptotic properties.…”

Section: A Definition and Building Of The Real-valued If V S And Bp V Smentioning

confidence: 99%

“…In the papers [21]- [26], the triangular form of these functions was used and in [27] their interval valued triangular versions were proposed. Currently the most used are trapezoidal [28]- [34] and interval valued trapezoidal [35]- [41] µ(x) and ν(x) functions. The natural limitations concerned with the too simple triangular and trapezoidal shapes of µ(x) and ν(x) functions are currently overcoming by the use of piece-wise linear functions consisting of different numbers of pieces.…”

Section: Introductionmentioning

confidence: 99%

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The New Definitions of Intuitionistic and Belief-Plausibility Based Local Criteria With Interval and Fuzzy Inputs Applied to the Multiple Criteria Problem of a Raw Material Supplier Selection

2021

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The problems of the A − IF S and A − IV IF S theories are analyzed and to solve them, their Dempster-Shafer theory based redefinition is developed and a new concept called Belief-Plausibility number (BP N ) is introduced. The BP N can be applied beyond semantics of usual fuzzy sets and the A − IF S. Two main sources of uncertainty generating the A − IV IF S are considered: an uncertainty coursed by the membership and non-membership functions multiplicity and an uncertainty of inputs. For the fuzzy inputs, the definition of the fuzzy-valued BP N is proposed. The developed approach to treat interval-valued intuitionistic fuzzy objects and their Belief-Plausibility re-definitions allowed us to introduce a set of useful definitions. It is important that some of the them were not earlier mentioned in the literature. The corresponding new arithmetical operations with such objects are proposed. The practical usefulness of the introduced approach is illustrated by the solution of the real-world Fuzzy-Valued Belief-Plausibility multiple criteria problem of the raw material suppliers selection on the steel rolling plant. The obtained results allowed us to state that the introduced Belief-Plausibility approach can be successfully used in the analysis and applications independently, without the use of the A − IF S concepts. This approach owns visible advantages in comparison with the A − IF S based one.

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Section: New Representations Of Peace-wise Membership and Non-membership Functions Their Interval Extensions Based On The Revealed Sourcementioning

confidence: 99%

“…As it was stated in the previous section, one of the problem of the known IF V definitions [21]- [41] are the controversial asymptotic properties.…”

Section: A Definition and Building Of The Real-valued If V S And Bp V Smentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The New Definitions of Intuitionistic and Belief-Plausibility Based Local Criteria With Interval and Fuzzy Inputs Applied to the Multiple Criteria Problem of a Raw Material Supplier Selection

2021

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A new approach to the comparison of real, interval and fuzzy-valued intuitionistic fuzzy and Belief-Plausibility numbers

Sevastjanov

Dymova

Kaczmarek

2023

International Journal of Approximate Reasoning

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Ordering Methods of C-Control Charts With Interval Type-2 Intuitionistic Fuzzy Sets

Cited by 2 publications

References 10 publications

The New Definitions of Intuitionistic and Belief-Plausibility Based Local Criteria With Interval and Fuzzy Inputs Applied to the Multiple Criteria Problem of a Raw Material Supplier Selection

The New Definitions of Intuitionistic and Belief-Plausibility Based Local Criteria With Interval and Fuzzy Inputs Applied to the Multiple Criteria Problem of a Raw Material Supplier Selection

A new approach to the comparison of real, interval and fuzzy-valued intuitionistic fuzzy and Belief-Plausibility numbers

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